Waldschmidt constants for Stanley-Reisner ideals of a class of graphs

In the present note we study Waldschmidt constants of Stanley-Reisner ideals of a hypergraph and a graph with vertices forming a bipyramid over a planar n-gon. The case of the hypergraph has been studied by Bocci and Franci. We reprove their main result. The case of the graph is new. Interestingly, both cases provide series of ideals with Waldschmidt constants descending to 1. It would be interesting to known if there are bounded ascending sequences of Waldschmidt constants.Comment: 7 pages, 2 figure

The Wakefield Effects of Pulsed Crab Cavities at the Advanced Photon Source for Short-X-ray Pulse Generation

In recent years we have explored the application to the Advanced Photon Source (APS) of Zholents' crab-cavity based scheme for production of short x-ray pulses. As a near-term project, the APS has elected to pursue a pulsed system using room-temperature cavities. The cavity design has been optimized to heavily damp parasitic modes while maintaining large shunt impedance for the deflecting dipole mode. We evaluated a system consisting of three crab cavities as an impedance source and determined their effect on the single- and multi-bunch instabilities. In the single-bunch instability we used the APS impedance model as the reference system in order to predict the overall performance of the ring when the crab cavities are installed in the future. For multi-bunch instabilities we used a realistic fill pattern, including hybrid-fill, and tracked multiple bunches where each bunch was treated as soft in distribution

A Novel Target-Height Estimation Approach Using Radar-Wave Multipath Propagation for Automotive Applications

This paper introduces a novel target height estimation approach using a Frequency Modulation Continuous Wave (FMCW) automotive radar. The presented algorithm takes advantage of radar wave multipath propagation to measure the height of objects in the vehicle surroundings. A multipath propagation model is presented first, then a target height is formulated using geometry, based on the presented propagation model. It is then shown from Sensor-Target geometry that height estimation of targets is highly dependent on the radar range resolution, target range and target height. The high resolution algorithm RELAX is discussed and applied to collected raw data to enhance the radar range resolution capability. This enables a more accurate height estimation especially for low targets. Finally, the results of a measurement campaign using corner reflectors at different heights are discussed to show that target heights can be very accurately resolved by the proposed algorithm and that for low targets an average mean height estimation error of 0.03 m has been achieved by the proposed height finding algorithm

Integrals Over Polytopes, Multiple Zeta Values and Polylogarithms, and Euler's Constant

Let $T$ be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over $T$, one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in single zeta values. We obtain asymptotic expansions of the integrals, and of sums of certain multiple zeta values with constant weight. We also give related expressions for Euler's constant. In the final section, we evaluate more general integrals -- one is a Chen (Drinfeld-Kontsevich) iterated integral -- over some polytopes that are higher-dimensional analogs of $T$. This leads to a relation between certain multiple polylogarithm values and multiple zeta values.Comment: 19 pages, to appear in Mat Zametki. Ver 2.: Added Remark 3 on a Chen (Drinfeld-Kontsevich) iterated integral; simplified Proposition 2; gave reference for (19); corrected [16]; fixed typ

Higher Order Modes Damping Analysis for the SPX Deflecting Cavity Cyromodule

A single-cell superconducting deflecting cavity operating at 2.815 GHz has been proposed and designed for the Short Pulse X-ray (SPX) project for the Advanced Photon Source (APS) upgrade. A cryomodule of 4 such cavities will be needed to produce the required 2-MV deflecting voltage. Each deflecting cavity is equipped with one fundamental power coupler (FPC), one lower order mode (LOM) coupler, and two higher order mode (HOM) couplers to achieve the stringent damping requirements for the unwanted modes. The damping of the LOM/HOM below the beampipe cutoff has been analyzed in the single cavity geometry and shown to meet the design requirements. The HOM above the beampipe cutoff in the 4-cavity cyromodule, however, may result in cross coupling which may affect the HOM damping and potentially be trapped between the cavities which could produce RF heating to the beamline bellows. We have evaluated the HOM damping in the 4-cavity cryomodule using the parallel finite element EM code suite ACE3P developed at SLAC. We will present the results of the cryomodule analysis in this paper

Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter

We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth (see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions. Theorem B: The epsilon expansion of a hypergeometric function with one half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are ratios of polynomials. Some extra materials are available via the www at this http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected and a few references added; v3: few references added

Holomorphic Quantization on the Torus and Finite Quantum Mechanics

We construct explicitly the quantization of classical linear maps of $SL(2, R)$ on toroidal phase space, of arbitrary modulus, using the holomorphic (chiral) version of the metaplectic representation. We show that Finite Quantum Mechanics (FQM) on tori of arbitrary integer discretization, is a consistent restriction of the holomorphic quantization of $SL(2, Z)$ to the subgroup $SL(2, Z)/\Gamma_l$, $\Gamma_l$ being the principal congruent subgroup mod l, on a finite dimensional Hilbert space. The generators of the ``rotation group'' mod l, $O_{l}(2)\subset SL(2,l)$, for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates.Comment: 12 pages LaTeX (needs amssymb.sty). Version as will appear in J. Phys.

H\"older-continuous rough paths by Fourier normal ordering

We construct in this article an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/\alpha$-variation for any $\alpha\in(0,1)$. The method may be coined as 'Fourier normal ordering', since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies. In doing so, there appear non-trivial tree combinatorics, which are best understood by using the structure of the Hopf algebra of decorated rooted trees (in connection with the Chen or multiplicative property) and of the Hopf shuffle algebra (in connection with the shuffle or geometric property). H\"older continuity is proved by using Besov norms. The method is well-suited in particular in view of applications to probability theory (see the companion article \cite{Unt09} for the construction of a rough path over multidimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or \cite{Unt09ter} for a short survey in that case).Comment: 50 pages, 6 figure